Exercise
$\int\frac{2xe^{2x}}{\left(2x+1\right)^2}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((2xe^(2x))/((2x+1)^2))dx. Take out the constant 2 from the integral. Rewrite the fraction \frac{xe^{2x}}{\left(2x+1\right)^2} inside the integral as the product of two functions: xe^{2x}\frac{1}{\left(2x+1\right)^2}. We can solve the integral \int xe^{2x}\frac{1}{\left(2x+1\right)^2}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du.
Find the integral int((2xe^(2x))/((2x+1)^2))dx
Final answer to the exercise
$\frac{-xe^{2x}}{2x+1}+\frac{1}{2}e^{2x}+C_0$